The present invention relates to a sheet gripping arrangement of a rotary printing machine. Sheet gripping arrangements are known and widely utilized in rotary printing machines. A known sheet gripping arrangement has a sheet gripping element and a sheet gripper abutment member cooperating with one another. The sheet gripping element includes one holder which is loosely arranged on a gripper shaft and another holder which is fixedly arranged on the gripper shaft, wherein the holders are coupled with one another in a resilient manner. A gripper finger cooperating with the gripper shafts is also provided. Such a construction is disclosed, for example, in the U.S. Pat. No. 2,599,776. The above-described construction possesses, however, the disadvantage in the fact of the circular movement of the sheet gripping element and the partial embedding of the gripping element tip into the elastically deformable sheet material and the material of the gripper abutment member. As a result the displacement of the sheet between the gripper abutment member and the gripping element cannot be excluded and thereby a position accurate delivery of the sheet between the sheet gripping arrangement of two cylinders is not guaranteed.